Mathematical Modelling of the Sterile Insect Technique Using Different Release Strategies

Anis Ben Dhahbi,Yassine Chargui,Salah Mahmoud Boulaaras,Sana Ben Khalifa,Faisal Alresheedi,Waleed Koko,Sundarapandian Vaidyanathan

doi:10.1155/2020/8896566

Abstract

We study simple mathematical models for the dynamics of interactive wild and sterile insect populations. As well as being mathematically tractable, these models can be used as first approximations to real situations occurring with the Sterile Insect Technique (SIT) in which sterile males are released to reduce or eradicate a pest population. This is a method of biological control which can effectively help contain the spread of many pest insects such as the Red Palm Weevil (RPW). Models formulated in this paper are continuous-time, include a strong Allee effect that captures extinction events, and incorporate different strategies of releasing sterile insects. We perform basic studies of dynamical features of these models, with an emphasis on the condition of excitation, and the impact of the different release methods is investigated. Our findings are also demonstrated with some numerical examples.

Highlights

In recent years, there has been a rapid rise in the use of biological methods for the control of insect pests
Such a technique constitutes a biological control process that disturbs the natural reproduction of the insect pests. is is carried out by using chemical or physical or other radical procedures to treat male insect pests to make them infertile, so they become unable to reproduce regardless of their sex drive. e infertile males are introduced to the environment and compete for mates with fertile males, such that interaction between sterilized males and any female wild insect pests will not lead to any insect reproduction, thereby disrupting the natural reproductive process of the population
This work studies relatively simple mathematical models describing the dynamics of interactive wild and sterile insect populations, occurring within the Sterile Insect Technique (SIT). e latter is a method of biological control, in which sterile males are released to reduce or eradicate a pest population, which can effectively help contain the spread of many pest insects such as the Red Palm Weevil (RPW)

Summary

Introduction

There has been a rapid rise in the use of biological methods for the control of insect pests. Is method, introduced initially by Knipling [1], consists in releasing high numbers of sterilized males into the environment Such a technique constitutes a biological control process that disturbs the natural reproduction of the insect pests. E former involve the release of genetically engineered insects (that have a lethal gene in their genome in the RIDL strategy), while the latter utilizes the Cytoplasmic Incompatibility (CI) property of the Wolbachia bacterium [3,4,5] These bacteria have the property to alter the sperm of infected males making it unable to fertilize uninfected eggs.

The General Model

Constant Release Rate

Release Rate Proportional to the Wild Population

Saturating Proportional Release Rate

Conclusion